That graph makes it clear that there are a whole lot of relatively low cost areas that, one would assume, don't have much of a housing shortage and a relatively small number of cities where housing costs are high to very high. Presumably people who don't have a specific, often employment-related, reason to live in one of those high-cost areas would not do so.
A fixed UBI makes moving to low cost areas very appealing. This lowers housing prices in the hot spots and raises wages in high cost areas. Net results city's become less packed and far more affordable.